I am a newbie trying to do the same to create my own drum covers of different songs. There are of course a few methods that springs to mind and most of them depends on your hardware in your studio. I have a mixer that is connected to my audio interface. Thus, I can run the streaming on another device and use this device's output as input to one channel on the mixer.
But if you only have your PC with S1, then you need to setup what is called loopback recording. Some audio interfaces support this, and some don't. So it would be wise to check if your audio interfaces supports this before venturing down this road.
If it does, this article describes the process of setting this up with Presonus audio interfaces. I guess the procedure is somewhat the same for other audio interfaces. Good luck.
Best regards
Trond Kvalo